The world number two dominated from start to finish against the youngster and eventually came through 6-1 6-2 6-3 to set up a clash with big-serving Sam Groth, currently ranked 67th.
It was also a great day for Britain’s number one women’s player as Johanna Konta produced an upset to dispatch Venus Williams 6-4 6-2.
For Murray it was a routine display against the highly-rated six-foot-six German as he broke serve six times and took little more than two hours to wrap up the win.
And the Scot admits it was a relief to get off the court and out of the heat early as he also waits on news from home, with the birth of his first child expected any time.
"I don't have any news because I've just come off the court," he said. "I'm hoping my phone hasn't been buzzing in my bag but Kim will message the team if anything happens in any of the matches.
"It got tough at the end and there were a lot of long games and rallies. Alex fought hard and made it very competitive. It was hot so I was glad to get it done in three sets."
Konta’s performance also appeared routine, though on paper it was anything but against the seven-time Grand Slam singles winner.
The British number one took 79 minutes to book her spot in the second round where she will face China’s Zheng Saisai.
"It's irrelevant how old she is because she's such a champion with so much experience and knowledge," said Konta.
"Even if she's playing with one leg out there, you've got to really take care of things on your own because she's an incredible player. I have all the respect for her in the world."
Elsewhere it was a difficult day for Britain’s other players with Dan Evans going out in three sets to Feliciano Lopez 6-1 6-0 6-4 and Aljaz Bedene losing in three to America’s Steve Johnson 6-3 6-4 7-6 (7-3).